Problem: Convert $\dfrac{32}{27}$ to a mixed number.
First, divide the numerator by the denominator. $32 \div 27 = {1}\ \text{ R } {5}$ So the improper fraction has $1$ wholes in it, which is equal to ${1} \times \dfrac{27}{27} = {\dfrac{27}{27}}$ This quotient $1$ is the whole number part of the mixed number. We also have a remainder of $5$ , though. That represents the $\dfrac{{5}}{27}$ remaining from the improper fraction; it wasn't enough to be another whole number. The converted mixed fraction is ${1}\ {\dfrac{5}{27}}.$ Note that if we add up the two pieces of our mixed fraction, ${\dfrac{27}{27}} + {\dfrac{5}{27}}$, we get the original improper fraction $\dfrac{32}{27}$.